B737 flight crew at FL180 reports TCAS RA with opposite direction King Air at 17500 FT. Evasive action was taken by climbing.

Narrative

[I] was working as the pilot monitoring. Aircraft is a new aircraft to the fleet and no equipment abnormalities were detected during the pre-flight; flight or after landing. Center advised to descend to FL180 and crew commenced descent after acknowledging to descend. Shortly before reaching FL180; ATC issued a traffic advisory of a Beechcraft King Air at 17;500 FT. We leveled at FL180. [We] reported to ATC that traffic was not in sight looking for traffic. Shortly thereafter; ATC issued another traffic advisory and the TCAS also began reporting 'Traffic.' King Air traffic was observed on TCAS approximately 10 miles ahead and altitude on TCAS indicated 300 FT below on a direct course. Immediately after the 'Traffic' advisory; the TCAS began issuing a resolution advisory to climb. We immediately began a climb in accordance with RA procedures listed in the (airline and fleet) QRH. [I] notified ATC that we would be vacating FL180 due to a TCAS resolution advisory. At the conclusion of the resolution advisory; the intruder aircraft was reported by TCAS to be 300 FT below; at FL181 based upon the flight's altitude of 18;400 FT. The intruder aircraft passed to the right side of the aircraft and was visually observed to be approximately 300 FT below and offset by approximately 500 FT. The aircraft looked like a King Air 90 and ATC addressed the aircraft as so. Both Captain and First Officer altimeters on flight indicated 18;000 FT with no error or deviation and the ISFD (Integrated Standby Flight Display) indicated same before the event. At the conclusion of the event both altimeters indicated 18;400 FT and the ISFD indicated no difference. After landing; the altimeters were checked against the field elevation with the altimeter setting of 29.92 applied. No deviation from tolerances was noted. [We] requested the full call sign of the aircraft to include in this report; ATC declined to provide the information. Flight continued and landed without incident. VMC conditions prevailed and we were vigilant for other traffic. ATC should have applied better traffic separation between the King Air; which was operating in Class E Airspace; and we were operating in Class A Airspace.